Analisi delle serie storiche per le quote di carbonio dell'Emissions Trading System europeo

Time series analysis is a highly significant field in statistics as it allows us to examine the historical evolution of a phenomenon over time. The purpose of this analysis is to identify a stochastic process that provides a suitable model for the observations, which can also be used for predictive purposes. In the course of the paper, the details of various classes of processes, both stationary and non-stationary, are presented. In particular, the ARMA processes are introduced, which are used for stationary time series and consist of an autoregressive component (AR) and a moving average component (MA). Subsequently, several classes of processes are introduced for handling heteroskedastic time series. These include the ARCH, GARCH, and EGARCH processes, which provide suitable models for volatility. These processes are then applied to assess and analyze the volatility of daily prices of European Carbon Allowances under the European Union Emissions Trading System (EU ETS), with a focus on Phase 4 (2021-2023). The EU ETS is a system introduced in Europe with the aim of achieving decarbonization goals, to which major emitter categories must adhere. Different models are estimated and the joint ARMA(5,1)-GARCH(1,1) model for the timeserie without the trend component, exhibits a superior ability to describe the price volatility. In this model, the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are lower than other models, and all its coefficients are significative (p < 0.05). Moreover, the standardized residuals are uncorrelated and their distribution is adequate. i